x2-18x-81=2526

Solution for x2-18x-81=2526 equation:

x2-18x-81=2526

We move all terms to the left:

x2-18x-81-(2526)=0

We add all the numbers together, and all the variables

x^2-18x-2607=0

a = 1; b = -18; c = -2607;
Δ = b2-4ac
Δ = -182-4·1·(-2607)
Δ = 10752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10752}=\sqrt{256*42}=\sqrt{256}*\sqrt{42}=16\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-16\sqrt{42}}{2*1}=\frac{18-16\sqrt{42}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+16\sqrt{42}}{2*1}=\frac{18+16\sqrt{42}}{2}
$